Prior art systems for target tracking involve estimating the state of a linear system in the presence of measurement and model uncertainties. These uncertainties may result from instrumentation sources and a part of the system state whose behavior is unknown. These unknown behaviors may be represented as a bias vector. In the restricted case where the bias is defined as the acceleration of a target, the following results hold. Non-maneuvering targets can be accurately tracked with a constant velocity filter. To keep the performance of the filter satisfactory, it is necessary to treat the bias as part of the system state. This will lead to an augmented state filter model. However, the computational cost increases with the dimension of the filter. Because of this added cost, many targeting systems simply use a constant velocity target model and ignore any unknown bias, that is, acceleration of the target.
However, when the target maneuvers, the accuracy of the position and velocity estimates provided by a constant velocity filter can degrade significantly. Furthermore, for a target undergoing a large maneuver, the target track may be lost because the constant velocity filter assumes target dynamics whose acceleration is zero-mean. To reduce the effect of the model's mismatch problem, the target acceleration is included as part of the target state in some tracking systems. A system using this approach of a constant acceleration model is capable of tracking maneuvering targets. However, such a filter provides less accurate estimates than the constant velocity filter when the target is not maneuvering. In addition, a constant acceleration model is significantly more expensive in terms of computational time and memory than the constant velocity model.
Another approach to tracking maneuvering targets is the variable dimension (VD) filter. In this approach, a constant velocity filter is used until a maneuver is detected. Then the filter state is augmented to include the acceleration as part of the state and the tracking is performed with the augmented state model until the maneuver disappears. At that time, a constant velocity filter is used again. This approach allows better tracking performance in both maneuvering and non-maneuvering situations than the use of either a constant velocity or a constant acceleration model alone. However, this approach has its disadvantages also. First, when the filter switches models, it goes through a transient period in which target estimates are poor. Second, the refiltering of measurements stored before the maneuver was detected result in a processing delay and a large peak demand for computations. As a result, the variable dimension filter is not suitable for real time combat systems. Third, the acceleration must approach zero before the filter model can be switched from the constant acceleration model to the constant velocity model. Since the acceleration estimates have a slower response to a maneuver than the velocity estimates, the switch to constant velocity filtering will be significantly delayed. Fourth, the use of the augmented state filter is expensive in terms of computation time and memory. Because of these shortcomings, it is clear that another approach to the problem of accurately tracking maneuvering targets is needed.